Hard-potential singularities and the threshold for global regularity

Determine the range of hard-potential exponents $\gamma$ for which Pauli exclusion is sufficient to yield global regularity for the Landau–Fermi–Dirac equation, and ascertain whether singularities analogous to those of the classical Landau equation occur for sufficiently hard potentials.

Background

The paper proves global regularity for the Coulomb potential by exploiting the Pauli exclusion bound, but the corresponding argument does not close for larger interaction exponents. Existing results for the classical Landau equation exhibit finite-time implosions for sufficiently hard potentials even when the distribution remains bounded. The authors conjecture that analogous singularities may occur for the Landau–Fermi–Dirac equation and explicitly identify the determination of the exponent range for global regularity as an open problem.

References

We conjecture that analogous singularities may occur for the LFD equation with sufficiently hard potentials. Determining the range of $\gamma$ for which Pauli exclusion is sufficient to yield global regularity remains an interesting open problem.

— Global smooth solutions to the inhomogeneous Landau-Fermi-Dirac equation  (2608.31071 - Golding et al., 31 Aug 2026) in Section 1, subsection “Propagation of Decay”